The Digital-to-Analogue converter (DAC) finds wide application in electronics and functions to convert digital data into an analogue signal, which is the reverse function of the Analogue-to-Digital converter (ADC). Although typically requiring more complex equipment, digital data can be stored, transmitted and manipulated with minimal degradation as compared to analogue signals. It is therefore common to convert analogue signals to digital data in order to benefit from this. However, for many applications, the digital data must ultimately be converted back to an analogue signal for end use.
A particular example is in the transmission and processing of audio signals. Sound waves from an original source may be captured by a microphone device and converted to an analogue electrical signal. Using an ADC, this can then be converted to a digital stream, which can be stored, transmitted or otherwise processed. However, a DAC is then required to convert the digital signal to an analogue electrical signal for driving an earphone or loudspeaker amplifier to produce actual sound (air pressure waves).
Various formats exist for storing and transmitting digital data according to the particular application. For example, a common format used to store video and audio data is MPEG-4, which is a digital multimedia format that allows streaming over the internet.
Another common format for high quality audio is pulse code modulation (PCM), which relates to a method for digitally representing sampled analogue audio signals. In this format, the analogue signal is sampled at uniform intervals and each sample is quantised to the nearest value within a range of digital steps. The resulting PCM stream is characterised by a sampling rate, which is the number of times per second the original audio signal is sampled, and the bit depth, which determines the number of possible digital values that can be used to represent each sample.
Digital-to-Analogue converters (DACs) can be realised in a number of ways. For linear PCM (LPCM) two architectures have commonly been used, namely: a) flash conversion where a digital word is converted to an analogue output directly at the sampling rate, and b) oversampling converters, which have become most common in integrated converters for audio.
FIG. 1 illustrates the internal block diagram of a typical oversampling integrated-circuit Digital-to-Analogue converter (DAC) 10. The input PCM stream 11 is first upsampled by an upsampling filter 12. Conversion then takes place in a high-speed delta-sigma modulator 13 feeding a DAC 14 to provide the output analogue signal 15.
The modulator operates on a narrow-word (3 to 8 bits) up-sampled PCM stream, often at a rate between 3 to 13 MHz. Commonly, the modulator 13 will run at an integer multiple of the incoming data rate. This modulator architecture is chosen because it is efficient to integrate on silicon. In a practical device, the analogue output of the modulator may be single-ended or balanced, current or voltage sources. Incoming linear PCM data for audio may commonly use sample rates in the range 32-384 kHz with precision in the range 16-32 bits.
In FIG. 1 we see that there is an interpolation upsampling filter structure 12 matching the rate of the incoming PCM signal 11 to that of the modulator 13. For integration efficiency the interpolation structure often takes the form of a multistage cascade of filters performing the up-sampling process in a series of steps. The sampling rates so interpolated in this structure may or may not have an integer relationship.
For designs intended for very high-performance, the cascaded interpolation filters can present limitations. For example, these may include one or more of the following: the form of the convolved impulse response of the cascaded filters; frequency response ripple; aliasing errors; quantisation noise and quantisation distortion through inadequate dithering of the filter or modulator stages. For these reasons, even where proportionally high-frequency content is not present relative to the Nyquist frequency, higher audio sample rates such as 96, 192 or 384 kHz, which reduce the number of interpolation stages, can result in superior sound.
Some converters intended for high performance allow direct input to the modulator, and in these cases rely on a signal which is already suitably up-sampled, dithered and quantised, which requires significant computational resource. Generally, economic considerations result in most applications using integrated filters.
A product designer who wishes to extract higher sound quality can take relatively simpler steps to ameliorate some properties of the upsampling filters and modulator. Such application improvements include preceding the converter with a so-called ‘apodising’ filter which is arranged to have a sub-Nyquist frequency transmission null, so as to prevent pre- and/or post-ringing on a transient. This type of filter is described in Craven, P. G., ‘Antialias Filters and System Transient Response at High Sample Rates’, J. Audio Eng. Soc., Vol. 52, No. 3, pp. 216-242, (March 2004).
The performance of a reproducing chain may also be improved by incorporating the DAC, its analogue and digital filters into a hierarchical scheme in which some or all of the upsampling stages can be performed in a cascade of simple stages based on triangular or B-spline kernels. This approach is described in Stuart, J. R., Craven, P. G., ‘A Hierarchical Approach to Archiving and Distribution’, 137th AES Convention, Los Angeles (October 2014). For example, such a cascade may use a simple triangle kernel for filter upsampling a signal from 192 kHz to 384 kHz, as described in Pohl, V., Yang, F., Boche, H., ‘Causal Reconstruction Kernels for Consistent Signal Recovery’, EUSIPCO, Bucharest, pp. 1174-1178, (2012).
One limitation to implementing systems based on the hierarchy of B-spline and/or triangular kernels is that available integrated devices may be limited to incoming data rates such as 96 or 192 kHz, thereby limiting the chain length, as noted by Stuart, J. R. and Craven, P. G. in ‘A Hierarchical Approach to Archiving and Distribution’, 137th AES Convention, Los Angeles (October 2014).
Applications seeking high-quality sound may also use dither or add a similar low-level uncorrelated noise to the incoming signal, at a level somewhat higher than the least-significant bit (LSB), to mask the subjective effects of quantisation errors in the integrated converter. Such a noise signal may be spectrally shaped to minimise its audibility.
Some examples of noise shaping and use of dither are described in Widrow, B., Kollár, I., Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications, CUP, Cambridge, UK, ISBN: 0521886716 (2008), also in Gerzon, M. A., Craven, P. G., Stuart, J. R., and Wilson, R. J., ‘Psychoacoustic Noise Shaped Improvements in CD and Other Linear Digital Media’, AES 94th Convention, Berlin, preprint 3501 (March 1993), and finally in Stuart, J. R., and Wilson, R. J., ‘Dynamic Range Enhancement using Noise-Shaped Dither at 44.1, 48 and 96 kHz’, AES 100th Convention, Copenhagen (1996).
Other performance limitations in an integrated-circuit DAC include thermal noise and non-linearity arising in the analogue stages. The signal-to-noise ratio can be improved by up to 3 dB by using two identically-driven DACs whose outputs are summed in the analogue domain (so-called ‘mono mode’). In a further refinement, by arranging for the input signals to the two converters to be inversely related and for the analogue signals to be subtracted, even-order non-linear distortion can be reduced by partial cancellation.
However, notwithstanding the developments described above, there remains a need for improved digital-to-analogue converter devices, which address the problems prevalent in more conventional DAC devices. This is particularly true for applications involving high quality sound.